<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">C</mi></mrow></semantics></math></inline-formula>-Semigroups and Their Induced Order

Abstract

Let C⊂Np be an integer polyhedral cone. An affine semigroup S⊂C is a C-semigroup if |C∖S|+∞. This structure has always been studied using a monomial order. The main issue is that the choice of these orders is arbitrary. In the present work, we choose the order given by the semigroup itself, which is a more natural order. This allows us to generalise some of the definitions and results known from numerical semigroup theory to C-semigroups.

Keywords

• C -semigroup%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline"><inline-formula> <mml:math id="mm99999"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">C</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-semigroup
• Wilf’s conjecture
• commutative monoids